Answer
$ŷ=-4.4+9.110x_1+4.294x_2+3.767x_4$
There is enough evidence that there is a linear relation between all three explanatory variables with calories.
Work Step by Step
Let's remove the explanatory variable sugar from the model.
In MINITAB, enter the fat values in C1, the protein values in C2, the carbs values in C4 and the calories values in C5.
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C5 in "Responses" and C1 C2 C4 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C5 is $ŷ$ (calories), C1 is $x_1$ (fat), C2 is $x_2$ (protein) and C4 is $x_4$ (carbs).
$ŷ=-4.4+9.110x_1+4.294x_2+3.767x_4$
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
$t_0=34.57$ with a P-value $\lt0.001\ltα=0.05$. Reject the null hypothesis.
2) $H_0: β_2=0$ versus $H_1: β_2\ne0$
$t_0=6.77$ with a P-value $=0.002\ltα=0.05$. Reject the null hypothesis.
4) $H_0: β_4=0$ versus $H_1: β_4\ne0$
$t_0=14.28$ with a P-value $\lt0.001\ltα=0.05$. Reject the null hypothesis.
